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JOURNALS // Algebra i logika // Archive
Algebra Logika, 2005 Volume 44, Number 3, Pages 261–268 (Mi al110)
This article is cited in 15 papers

Elementary Theories for Rogers Semilattices

S. A. Badaeva, S. S. Goncharovb, A. Sorbic

a Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
c Dipartimento di Scienze Matematiche ed Informatiche Roberto Magari, Università degli Studi di Sienna

Abstract: It is proved that for every level of the arithmetic hierarchy, there exist infinitely many families of sets with pairwise non-elementarily equivalent Rogers semilattices.

Keywords: arithmetic hierarchy, Rogers semilattice, elementary theory.

UDC: 510.55

Received: 25.02.2003
Revised: 12.07.2004


 English version: Algebra and Logic, 2006, 44:3, 143–147

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© Steklov Math. Inst. of RAS, 2025